For both assuring product quality of a sheet and producing the sheet stably, excellent flatness is required. Accordingly, properly managing flatness in a sheet production process has been a matter of interest since heretofore.
Values referred to as “differential elongation rate” and “steepness” are commonly used as indexes representing flatness.
The differential elongation rate Δε is the difference over a certain range in a length direction of a sheet (i.e., the traveling direction in a production line) between an elongation rate εCENT of a central portion in a width direction of the sheet and an elongation rate εEDGE elsewhere than the sheet width direction central portion (generally, a vicinity of an edge). The differential elongation rate Δε is represented by the following mathematical expression (2).Δε=εCENT−εEDGE  (2)
The steepness λ is defined, using a sheet wave height δ and a pitch P, as λ=δ/P. Because the shapes of sheet waves are close to sine waves, the differential elongation rate Δε and the steepness λ (%) have a well-known relationship represented by the following mathematical expression (3).
                    λ        =                  {                                                                                          +                                          2                      π                                                        ⁢                                                                                                          Δ                        ⁢                                                                                                  ⁢                        ɛ                                                                                                          1                      /                      2                                                        ×                  100                  ⁢                                                                          ⁢                                      (                                                                  if                        ⁢                                                                                                  ⁢                        Δ                        ⁢                                                                                                  ⁢                        ɛ                                            ≧                      0                                        )                                                                                                                                            -                                          2                      π                                                        ⁢                                                                                                          Δ                        ⁢                                                                                                  ⁢                        ɛ                                                                                                          1                      /                      2                                                        ×                  100                  ⁢                                                                          ⁢                                      (                                                                  if                        ⁢                                                                                                  ⁢                        Δ                        ⁢                                                                                                  ⁢                        ɛ                                            <                      0                                        )                                                                                                          (        3        )            
A production line for hot-rolled steel sheet, which is an example of a sheet, commonly consists of, for example, a heating furnace, a roughing mill, a finishing mill, a cooling zone, and a coil winder. A steel slab heated in the heating furnace is rolled by the roughing mill and formed a steel slab (a rough bar) of 30 to 60 mm thick. Then, the steel slab is rolled by the finishing mill, which is equipped with six or seven rolling stands, and formed into hot-rolled steel sheet with a thickness aimed by a customer. The hot-rolled steel sheet is cooled in the cooling zone and wound by the coil winder.
Producing hot-rolled steel sheet with excellent flatness is important for both assuring product quality and maintaining high productivity, in stably feeding the sheet to the finishing mill, winding the sheet at the coil winder and so forth. Flatness failures of hot-rolled steel sheets that arise subsequent to the finishing mill are caused by elongation rate that is uneven in the sheet width direction occurring in the finishing mill and the cooling zone. Accordingly, methods have been proposed for producing hot-rolled steel sheet with excellent flatness, including: a method of installing a flatness gauge, a sheet thickness profiler or the like between the rolling stands that constitute the finishing mill or at the exit side of the finishing mill and performing feedback control of work roll benders of the rolling stands in response to measured values; and a method of learning control of setup conditions such as work roll shift positions, load distribution in the finishing mill and the like. The above-mentioned control methods are described in, for example, Japanese Patent Application Laid-Open (JP-A) No. H11-104721. A further method has been proposed, of situating a flatness meter at the exit side of the cooling zone and performing feedback control of cooling water quantities from cooling nozzles of the cooling zone in response to measured values. To realize the control methods mentioned above, methods and devices for measuring the flatness of hot-rolled steel sheet traveling at high speed, between the rolling stands, at the exit side of the finishing mill, or at the exit side of the cooling zone, have been proposed and employed in practice.
A method for measuring the flatness of hot-rolled steel sheet that is conventionally known is a method of projecting a linear pattern composed of a plurality of light lines that extend in the sheet width direction onto the surface of hot-rolled steel sheet that is being hot-rolled and traveling, capturing an image of the linear pattern with a two-dimensional camera from a direction that is different to the direction of projection of the linear pattern and, on the basis of distortions of the linear pattern in the captured image, measuring the surface shape of the hot-rolled steel sheet and hence the flatness. For example, JP-A No. 2008-58036 recites a method of using a slide on which a high-density linear pattern is drawn, projecting the high-density linear pattern composed of a plurality of light lines extending in the sheet width direction onto a sheet surface, capturing an image of the same with a camera and, on the basis of distortions of the linear pattern in the captured image, measuring the surface shape of the sheet and hence the flatness. With this method, because a high-density linear pattern is projected, a measurement resolution (spatial resolution) of the surface shape is high and accurate measurement of the surface shape of the sheet may be expected.
The shape measurement method as described in JP-A No. 2008-58036 is commonly referred to as the grating pattern projection method. It is not limited to measuring surface shapes of steel sheet but is used for a variety of applications.
FIG. 1 is a diagram schematically illustrating an equipment structure example for implementing the grating pattern projection method. As illustrated in FIG. 1, in the grating pattern projection method, a grating pattern (a light and dark pattern) PT′ is projected onto a sheet surface from diagonally above the sheet surface, using a projector PR equipped with a light source LT, a slide SL on which the grating pattern (generally a linear pattern) PT is drawn, and a focusing lens LN. An image of the grating pattern PT′ projected onto the surface of the sheet PL is captured using a two-dimensional camera CA, in a direction that is different from the projection direction of the grating pattern PT. In this process, if the surface shape of the sheet varies, inclination angles of the surface of the sheet PL vary, and a pitch PC (generally, the spacing of light lines composing the linear pattern) of the grating pattern PT′ in the image captured by the camera varies in accordance with the inclination angles of the surface of the sheet PL. A relationship between inclination angles of the sheet surface and the pitch PC of light portions of the grating pattern PT′ in the captured image can be geometrically calculated. Therefore, if the pitch PC of light portions of the grating pattern PT′ in the captured image is measured, the inclination angles of the sheet surface can be calculated on the basis of the aforementioned relationship with these measurement results (i.e., the relationship between the inclination angles of the sheet surface and the pitch PC of the light portions of the grating pattern PT′ in the captured image). The surface shape of the sheet PL may be calculated by integrating the calculated inclination angles. The relationship between the inclination angles of the surface of the sheet PL and the pitch PC of the light portions of the grating pattern PT′ in the captured image includes, as a parameter, a pitch PC of the light portions of the grating pattern PT′ in a captured image of the grating pattern PT′ that is acquired from a standard sheet (a calibration sheet) that has a flat surface shape.
As methods that employ the above-described grating pattern projection method to measure the flatness of sheets, the present inventors have proposed the methods described in Japanese Patent Nos. 4,666,272 and 4,666,273. According to these methods, if an image capturing means is equipped at a location at which regular reflection light from a light and dark pattern projected onto the surface of a sheet with strong regular reflectivity can be detected, in order to reduce the space required for arrangement of a measuring device, the flatness of the sheet may be accurately measured. However, these methods presume that the flatness is measured mainly at the exit side of a finishing mill.
Ordinarily, a looper for controlling tension in a steel sheet is equipped between rolling stands structuring a finishing mill. The tension in the steel sheet is controlled by altering a looper angle. When the looper angle is changed, a sheet passage route of the steel sheet traveling between the rolling stands changes. Thus, when the looper angle is changed, an inclination angle and height (vertical direction position) of the steel sheet surface change.
Therefore, when the flatness of the steel sheet between the rolling stands is being measured, even if the steel sheet has, for example, a flat surface shape, the pitch of the light portions of a light and dark pattern in a captured image changes in accordance with alterations of the looper angle, causing measurement errors.
It has been proposed, for example, in Japanese Patent No. 4,797,887, to prepare a plurality of pitches (calibration values) of the light portions in a light and dark pattern from a plurality of standard sheets (calibration sheets) associated with different heights of a steel sheet surface in advance, to measure the height of a steel sheet, and to use the calibration value corresponding to the measured height.
However, even if the method described in Japanese Patent No. 4,797,887 is employed when measuring the flatness of a steel sheet between rolling stands, this method only takes account of the height of the steel sheet surface. Situations in which both the height of a steel sheet surface and an inclination angle of the steel sheet surface are changed when the looper angle is changed are not considered. Moreover, the necessary preparation of a plurality of calibration values takes time.